Abstract:The process of uncertainty evaluation methods based on GUM serials and Bayesian analysis is compared, and it is derived that GUM uncertainty evaluation is based on measurement equation, and a forward uncertainty evaluation method, while Bayesian analysis is an inverse uncertainty evaluation based on observation equation. A probabilistic approach to analysis and comparison is used to the two approaches. It’s concluded that for linear model and with non-informative prior for the measurand both analysis can be applied and get the same result, but for non-linear model, only GUM S1 method and Bayesian analysis give the same result. The results are illustrated by examples.
[1]BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement[S].International Organization for Standardization, Geneva, Switzerland, 2008.
[2]BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Guide to the Expression of Uncertainty in Measurement. International Organization for Standardization, Evaluation of measurement data-Supplement 1 to the “Guide to the expression of uncertainty in measurement”-, Propagation of Distribution Using a Monte Carlo method[S]. International Organization for Standardization, Geneva, Switzerland, 2008.
[3]BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML. Evaluation of measurement data-Supplement 2 to the “Guide to the expression of uncertainty in measurement”-Extention to any number of output quantities[S]. International Organization for Standardization, Geneva, Switzerland, 2011.
[4]费业泰. 误差理论与数据处理[M]. 北京:机械工业出版社,2015.
[5]倪育才. 实用测量不确定度评定[M]. 北京:中国计量出版社,2004.
[6]Weise K, Wger W. A Bayesian theory of measurement uncertainty[J]. Measurement Science and Technology,1993,4(1):1-11.
[7]Lira I,Grientschnig D. Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty[J]. Metrologia,2010,47(3):334-336.
[8]Lira I, Wger W. Comparison between the conventional and Bayesian approaches to the evaluate measurement data[J]. Metrologia,2006,43(4): 249-259.
[9]Calonico D, Levi F, Michel R, et al. Bayesian inference of a negative quantity from positive measurement results[J]. Metrologia,2009,46(3): 267-271.
[10]胡红波,孙桥,杜磊. GUM S1与基于贝叶斯方法的不确定度评估比较[J]. 计量学报,2017, 38(4): 517-520.
[11]Possolo A, Toman B. Assessment of measurement uncertainty via observation equations[J]. Metrologia,2007,44(6): 464-475.
[12]韦来生,张伟平. 贝叶斯分析[M]. 合肥:中国科学技术大学出版社,2015.
[13]姜瑞,陈晓怀,王汉斌,等. 基于贝叶斯信息融合的测量不确定度评定与实时更新[J]. 计量学报,2017, 38(1): 123-126.